15-815 Automated Theorem Proving
Lecture 24: Completion

We discuss methods for deciding if a given equation follows
from a collection of universally quantified equations. The first
idea is that if we a reduction order that orients all equations
and the resulting system is confluent, then we can decide
equality between two terms by normalizing them and comparing
the normal forms for equality.

Often, we cannot directly find such a presentation but we
need to complete the set of rewrite rules in order
to make the confluent (while still respecting the reduction order,
of course). We present completion abstractly as a set of
inference rules, to be applied in the forward direction.